The strong coupling between light and matter gives rise to polaritons. Further coupling polaritons to phonons leads to the formation of hybrid polaromechanical systems. Recent experiments have achieved the strong coupling between polaritons and phonons in two configurations, namely, the magnon-photon-phonon and exciton-photon-phonon systems, which enables the control of mechanical motion via manipulating polaritons. Here, we present a polaromechanical cooling theory and explicitly show how two polaritons can be used to simultaneously cool two mechanical modes. The unique advantage of our protocol lies in the fact that the continuous tunability of the polariton frequencies over a wide range allows for the cooling of any two mechanical modes with their frequency difference falling within this range. We further discuss how to extend the theory to cool multiple mechanical modes. The protocol is designed for cooling mechanical motion in various emerging polaromechanical platforms, such as magnon-, exciton-, and plasmon-polaromechanical systems, which is the first step towards quantum states generation in these hybrid systems.